x^2-4.1x+2.2=0

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Solution for x^2-4.1x+2.2=0 equation: 


Simplifying
x2 + -4.1x + 2.2 = 0

Reorder the terms:
2.2 + -4.1x + x2 = 0

Solving
2.2 + -4.1x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-2.2' to each side of the equation.
2.2 + -4.1x + -2.2 + x2 = 0 + -2.2

Reorder the terms:
2.2 + -2.2 + -4.1x + x2 = 0 + -2.2

Combine like terms: 2.2 + -2.2 = 0.0
0.0 + -4.1x + x2 = 0 + -2.2
-4.1x + x2 = 0 + -2.2

Combine like terms: 0 + -2.2 = -2.2
-4.1x + x2 = -2.2

The x term is -4.1x.  Take half its coefficient (-2.05).
Square it (4.2025) and add it to both sides.

Add '4.2025' to each side of the equation.
-4.1x + 4.2025 + x2 = -2.2 + 4.2025

Reorder the terms:
4.2025 + -4.1x + x2 = -2.2 + 4.2025

Combine like terms: -2.2 + 4.2025 = 2.0025
4.2025 + -4.1x + x2 = 2.0025

Factor a perfect square on the left side:
(x + -2.05)(x + -2.05) = 2.0025

Calculate the square root of the right side: 1.41509717

Break this problem into two subproblems by setting 
(x + -2.05) equal to 1.41509717 and -1.41509717.


Subproblem 1
x + -2.05 = 1.41509717

Simplifying
x + -2.05 = 1.41509717

Reorder the terms:
-2.05 + x = 1.41509717

Solving
-2.05 + x = 1.41509717

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '2.05' to each side of the equation.
-2.05 + 2.05 + x = 1.41509717 + 2.05

Combine like terms: -2.05 + 2.05 = 0.00
0.00 + x = 1.41509717 + 2.05
x = 1.41509717 + 2.05

Combine like terms: 1.41509717 + 2.05 = 3.46509717
x = 3.46509717

Simplifying
x = 3.46509717


Subproblem 2
x + -2.05 = -1.41509717

Simplifying
x + -2.05 = -1.41509717

Reorder the terms:
-2.05 + x = -1.41509717

Solving
-2.05 + x = -1.41509717

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '2.05' to each side of the equation.
-2.05 + 2.05 + x = -1.41509717 + 2.05

Combine like terms: -2.05 + 2.05 = 0.00
0.00 + x = -1.41509717 + 2.05
x = -1.41509717 + 2.05

Combine like terms: -1.41509717 + 2.05 = 0.63490283
x = 0.63490283

Simplifying
x = 0.63490283


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.46509717, 0.63490283}

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